(m w[z]^4 - 2 m w[z]^2 + 1) w[2 z] + m w[z]^4 - 2 w[z]^2 + 1 == 0 /; w[z] == JacobiCD[z, m]

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["m", " ", SuperscriptBox[RowBox[List["w", "[", "z", "]"]], "4"]]], "-", RowBox[List["2", " ", "m", " ", SuperscriptBox[RowBox[List["w", "[", "z", "]"]], "2"]]], "+", "1"]], ")"]], " ", RowBox[List["w", "[", RowBox[List["2", " ", "z"]], "]"]]]], "+", RowBox[List["m", " ", SuperscriptBox[RowBox[List["w", "[", "z", "]"]], "4"]]], "-", RowBox[List["2", " ", SuperscriptBox[RowBox[List["w", "[", "z", "]"]], "2"]]], "+", "1"]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List["JacobiCD", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <mi> m </mi> <mo> &#8290; </mo> <msup> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> m </mi> <mo> &#8290; </mo> <msup> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <msup> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> cd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <times /> <ci> m </ci> <apply> <power /> <apply> <ci> w </ci> <ci> z </ci> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <ci> w </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> m </ci> <apply> <power /> <apply> <ci> w </ci> <ci> z </ci> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> m </ci> <apply> <power /> <apply> <ci> w </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ci> w </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> w </ci> <ci> z </ci> </apply> <apply> <ci> JacobiCD </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["m_", " ", SuperscriptBox[RowBox[List["w", "[", "z_", "]"]], "4"]]], "-", RowBox[List["2", " ", "m_", " ", SuperscriptBox[RowBox[List["w", "[", "z_", "]"]], "2"]]], "+", "1"]], ")"]], " ", RowBox[List["w", "[", RowBox[List["2", " ", "z_"]], "]"]]]], "+", RowBox[List["m_", " ", SuperscriptBox[RowBox[List["w", "[", "z_", "]"]], "4"]]], "-", RowBox[List["2", " ", SuperscriptBox[RowBox[List["w", "[", "z_", "]"]], "2"]]], "+", "1"]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List["JacobiCD", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]]]]

2001-10-29